Bonesetter's right, carbon this and foam that makes no odds compared to getting your weight off the front. Read about Jeff Jones take on it all on his site, he pretty much re-jigged mtbs a long time ago on that basic idea.

I can't really add much more to what's already been said.
I've had the XLT forks and I was always suprised at how much they did soak up, considering the consensus on Al forks is of teeth-rattling stiffness! Also, quoting Jeff Jones, I believe the Truss forks have absolutely no movement in them at all, but I suppose that does tie in much more with the rest of the frame design?
I did find On-Ones' steel forks fine, no problem. The Carbon ones frightened me with the amount of flex and flutter though!
On my last 26" I had a Continental Vapour 2.5 on a 47mm trials rim on the front, that worked beautifully in wet and dry (though not mud).
Also, ODI Longneck ST grips have always been a favourite and come in a little cheaper than the ESIs.

Bonesetter's right, carbon this and foam that makes no odds compared to getting your weight off the front. Read about Jeff Jones take on it all on his site, he pretty much re-jigged mtbs a long time ago on that basic idea.

+1 on this, then get a proper tyre on the front. Don't get hung up on weight, a bigger one will be better in every way.

Other than technique (e.g. heavy feet & loose hands etc) tyre choice is your main problem unless you're just riding towpaths etc. Try some modern big volume tyres run at a lower pressure, ideally tubeless but not essential. If you don't want to spend a lot of money something like a pair of On-One Chunky Monkey 2.4's would be a good start, or at least try one on the front at around 25psi. You might be pleasantly surprised.

ESI chunky grips also help in my experience and will offset some of the weight gained by the bigger tyres if that bothers you.

A Chunky Monkey is an excellent front tyre with rigid forks - I go a lot lower than 25psi though, more like 18 (and tubeless).
This, with a 29" front wheel and Singular Hummingbird forks is a nice combination - it works for me anyway.

Hijack, but related - Building up a rigid Swift for Mrs r at the moment. Thinking big tyres eg 2.4 Conti X King, certainly in the front, but not sure whether to take (i.e. give her) the weight penalty of say velocity blunt 35s over Crest/Arch EX for the extra volume. 2kg wheelset rather than 1600g

And would they mess up the tyre profile of a narrower tyre on the back?

I think most of us do. imo as long as your weight can go back when needed, bar height isn't that important. But generally as you rotate your seated position back around the BB (anticlockwise seat position change, from the drive-side on view) you'll be more comfy if your bars go up and back also.
Higher bars felt really odd to me at first but there's no way you'd get me to change them on my rigid bike now. Low enough to corner OK, keep raising them until you feel like you're too high then see if you can adjust to it. To me, swinging my hips forward a little in a corner or just bending my arms a bit makes as much difference as 1-2" on bar height but when it comes to straight-line control I'm better off with that up and back position. All personal stuff tho, if it doesn't feel right to you then it can be hard or impossible to adjust.

not sure whether to take (i.e. give her) the weight penalty of say velocity blunt 35s over Crest/Arch EX for the extra volume. 2kg wheelset rather than 1600g

Unless you're a whippet weenie, do it. My 29er wheels (P35s, Ardent EXOs) are way over 2kg and they're overall a much more fun wheelset than any light off-road wheels I've had. Take a tad more winding up but you get stronger anyway, they seem to flow much better once at speed. May depend on your riding area etc. I have a lot of singletrack locally where they're not the fastest to accelerate out of corners but they do seem to carry speed better overall, so I probably go into/through corners faster.
And 600g/35mm isn't a big rim by many people's standards now : )

A Chunky Monkey is an excellent front tyre with rigid forks - I go a lot lower than 25psi though, more like 18 (and tubeless).
This, with a 29" front wheel and Singular Hummingbird forks is a nice combination - it works for me anyway.

I agree, before I went 29+ I was running my Chunky Monkeys at around 18psi tubless and found them to be excellent. 25psi would be more wise if using tubes though.

If it was for me, I’d go big, but the it’s mrs r’s, bought so she can spend less effort keeping up in groups and have an easier time on the hills and clipping along on the flat. Current bike is the noughties steel 26" clockwork ltd. reissue jobby. Fun when the trail points down, but there’s something about it that means it drags, rides heavy, could be the actual weight, tubing, geometry, bearings, the tiny, tiny, outmoded wheels…

Wary of taking the Swift build too far down the “handles great, just needs a bit of effort to get it moving/up the hills” as that’s what we’re trying to get away from. The Swift is already a step down that road, but she tried one and liked the ride, liked the looks, didn’t like pulling the dually/knard combo up the hills. Thunder Burts on my stans 340s felt much easier, but more skittish.

I guess one option is to build up a blunt 35 wheelset, if she doesn’t get on with them, we can find something lighter for her and I can save the blunts for the odd occasion when I might need to take it out for a "safety check".

Well today went better. On bridleways so many more options for picking the lines. Let a bit of pressure out of the tyres, that helped, but inevitably ended up with a pinch flat before the day was out (ok, I was messing around a bit by then!)

Rode light, kept a looser grip on the bars, and did half the mileage. Felt great at the end of the day! I did put my thick gloves on for the descent (it was cold and raining on the fells today) and that made a big difference, definitely want thicker grips for my larger hands.

I'm sold on a wider front tyre and grips and reckon that will be it sorted. Also need a new rear calliper as I missed having no rear brake on a few sections A large order awaits on pay day!

Most importantly though, I had LOADS of fun and feel like I'm riding better for it.